Procurement scheduling for Assemble-to-Order systems

Due to the increasing complexity and diversity of customer demand, assemble-to-order (ATO) systems should account for more realistic factors in their procurement decisions. The classical literature offers analytical elegance but oversimplifies reality. This study bridges this gap by developing a multi-period procurement problem for multi-product ATO systems under scenario-based demand uncertainty, considering realistic factors like varying product prices, bill of materials (BOM) structures, multiple suppliers with different lead times and costs, and contract options provided by suppliers with different discount prices. A multi-stage stochastic programming model is formulated to maximize the profit of the ATO system by optimally making decisions on (i) pre-stocked inventory, (ii) supplier selection, (iii) contract signing with options, and (iv) assembly planning. To solve the model efficiently, we propose an exact Benders decomposition algorithm with tailored subproblem (SP) relaxation, valid inequalities, and Pareto-optimal cuts. Experiments based on real data validate the exact algorithm’s effectiveness. For large-scale instances, the proposed algorithm improves the objective value by 13.7% over Gurobi’s best-found solution within a one-hour time limit. To further accelerate the algorithm, we introduce an efficient scenario reduction method based on forward-looking distance matrices. The proposed reduction method is proven to be more effective than traditional approaches, improving solution quality by up to 15.4% while accelerating computation by a factor of 3.5. This study also provides managerial insights for contract design, pre-stocking strategies, and supplier selection. For example, decision-makers should negotiate with suppliers for more contract options in volatile markets, prioritize slow suppliers while maintaining a pool of fast suppliers as backups, and increase pre-stocked inventory for those with high and very high commonality.